MATHEMATICAL MODEL BASED OF TRANSFER FUNCTIONS FOR DYNAMIC OPERATIONS OF SUPERCHARGED ENGINE
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1 AEAIAL ODEL BASED O RANSER UNIONS OR DYNAI OERAIONS O SUERARGED ENGINE Salvaore ugurel BURIU + Univerity Dunarea e Jo of Galati, Roania, Rezuat: Lurarea rezinta oelul ateati entru oortarea inaia a otorului ieel uraalientat u turbooreor u rotatie libera oelul ateati e bazeaza e unoaterea arateritiilor ubiteelor riniale, aa u unt otorul roriu-zi, turbooreorul, galeria e aiie i evauare, intalatia e injetie arateritiile aetor ubitee unt unoute entru regiurile tationare e funtionare i in aroierea aetora, ua atele exerientale, e baza eterinarilor e tan oelul ateati ete exriat e euatia iferentiala e orinul oi are exria oortarea inaia a intregului ite Sunt tabilite funtiile e tranfer, are ot fi foloite entru reglarea autoata a intregului ite uvinte eie: otor ieel uraalientat, funtii e tranfer, funtionare in regi inai, regiuri netationare e funtionare Abtrat: e aer eal wit te ifferential equation exreing te ynai oeration of turboarge internal obution engine uing uerarger wit free rotation unit ateatial oel i bae on nowlege of te arateriti of ubyte, u a engine itelf, turboarger, exaut an intae anifol an te injetion yte to tationary regie ranfer funtion are eterinate, funtion tat are ue for aieving an ajuting autoati ontrol yte wi ontrol te oeration of te wole yte (engine) uner onieration eywor: uerarge ieel engine, tranfer funtion, ynai regie, unteay woring onition 1 INRODUION e aer reent te ateatial oel for alulatin tranfer funtion for te wole uerarge internal obution engine, wit free rotation uerarger unit ateatial oel i bae on ifferential equation an te tranfer funtion etablie, [8], [3], [4], [5], [6], [7], [] for ynai oeration of ubyte, a tey are exaut an intae anifol, injetion yte, engine itelf, turboarger [1], a art of internal obution engine, a own in figure 1 On te bai of tee equation reult te ynaial beavior of internal obution engine Uing tranfer funtion an buil autoati ontrol yte (ontroller) an ae it awar wit engine, u a exiting autoati governor for revolution DYNAI REGIE O DIESEL SUERARGED ENGINE We onier te following iagra (ig 1) wit te ubyte [8], [1], art of te uerarge internal obution engine, wit free rotation turboarger In tee iagra, ubyte are: - turbooreor; S Inj - uel injetion yte; G - ga turbine; Dieel - ieel engine itelf; AD - intae ie; EV - exaut ie; - angular ee of engine; - angular ee of turboarger; inj - angular ee of fuel injetion u; fuel onution for a ;, - te oition of ajutent atuator of turbooreor reetively turbine; a, inj AD SInj,il G EV Dieel g g ig1 Diagra for uerarge engine ubyte 18 EROENIA Sulient 1/13
2 a, - a flow of air aitte into te oreor; - a flow of air entering te intae anifol;,il - a flow of air entering te engine yliner; - atuator oition of te injetion u for ieel engine; g exaut ga a flow entering te exaut anifol; - exaut ga a flow entering te turbine; g - exaut ga a flow oing out in te environent Uing te ifferential equation etablie in [3], [4], [5], [6], [8], [] wi ae te ynaial oeration of ontitutive art near by te teay woring onition, it oible to aieve te ifferential equation for wole uerarge internal obution engine terefore te ynaial beavior Aoring wit [8], [3], [4], [5], [6], [7] an write: -- for Dieel engine itelf: eng eng (1) eng eng after ue Lalae tranforation: eng eng eng eng -- for injetion yte: a inj a inj after ue Lalae tranforation: a inj a inj -- for turboarger : Were: (3) J eng eng te after ue Lalae tranforation:, (3 ) te eng -- for intae anifol: te, a a t _ eng a a (4) eng a te after ue Lalae tranforation:, (1 ) () ( ) a a a a a (4 ) -- for exaut anifol: ev ev ev ev (5) ev after ue Lalae tranforation : ev ev ev ev ev (5 ) Were: ; (6) ; (7) S S R (8) S =angular ee for teay woring onition; = fuel onution for tey woring onition; =ajutent evie at onuer for teay woring onition; =te reure furnie by oreor for teay woring onition; =ga reure at te entrane of ga turbine for teay woring onition; (9) (1) (11) EROENIA Sulient 1/13 19
3 11 EROENIA Sulient 1/13, te S ter eng (1) tg J (13) tg t (14) tg t (15) tg tg (16) tg t (17),ilu te ter _ eng t (18) tg t t (19) a inj () inj _ a (1) tg tg () a t a (3),il a (4),il a (5),il a (6) a a n V (7),il a _ t (8) g ev t ev (9) g ev (3) g ev (31)
4 ev g (3) Vev (33) ev g n g (34) t _ ev J (g ) - eanial oent of inertia of te rotating eanial turboarger oonent, reue to it revolution axi: ( -1 ) - oon angular ee of te oreor an turbine; ( -1 ) - angular engine ee; J eng (g ) = eanial oentuu inertia of te obile eanial engine, reue to it revolution axi; te (N) = torque of engine; te R (N) torque to rive, te oule ut overoe te brae reitane brae; t (N)-- brae torque of oreor ; tg (N)-- torque of ga turbine; (g/) - oreor a flow rate; (g/) - ga turbine a flow rate; = te oition of ajutent evie for injetion u; atuator turbine ontrol oition; atuator oreor ontrol oition;, (g fuel/) fuel onution on at tationary running; (N/ ) - ga reure in te turbine entry; (N/ ) - flui reure at te oreor exit; () - flui teerature at te exit of te oreor; () - ga teerature at te entrane of ga turbine; (g fuel/) fuel onution on ; inex iniate tationary oerating regie; = atuator oreor ontrol oition at teay woring onition; = atuator turbine ontrol oition at teay woring onition; ( -1 ) - oon ee of te oreor an turbine at tationary running; teg (N) - turbine aft torque at tationary running; te (N) - oreor aft torque at tationary running; (N/ ) - ga reure in te turbine entry at tationary running; (N/ ) - flui reure at te oreor exit at tationary running; If te turboarger a not aequate ajutable evie (atuator), in te equation (1,,3,4,5) artiular onition i, reetively (1,,3,4,5 ), an reult equation: eng eng eng (35) eng a inj (36) a inj a a ev ev ev (37) a (38) ev (39) If we want to obtain te ifferential equation of te internal obution engine witout te aequate ajutent evie for an, it i neeary to olve te artiular equation yte reulting fro te general equation 35, 36, 37, 38, 39 igure, 3, 4, 5, 6 ow te trutural iagra for te turboarger engine itelf, te fuel injetion yte, te intae anifol, te exaut anifol an te turboarger In tee iagra te tranfer funtion are et out in retangle, te inut ignal on te left an te outut ignal on te rigt e inex nuber ae to oe inut ignal rereent te nuber of te trutural iagra were tat ignal oe out We onier te ineenent araeter an [8], an te unnown quantitie,,,, or te internal obution engine a te ubjet of autoati ajutent abiing by te revolution, i oniere to be te araeter wi ut be urue in tie: EROENIA Sulient 1/13 111
5 ; ; (4) Were: eng_ eng_ eng_ 1 at_inj_ u at_inj_ u (41) eng _ eng ainj a ev (4) e ifferential equation written in te oerational for, were te rotation i oniere a te objet of autoati ajutent, i a follow: (43) Or: eng _ eng_ eng_ 1 at_ inj_ u, 4 S 3 at_ inj_ u (44) engine engine engine,,, SInj, SInj, () () () ig Strutural iagra for te turboarger engine itelf,(), () () ig 3 Strutural iagra for te fuel injetion yte, 4 3,6 ev, It terefore lea to: a, a, at_inj_u at_inj_u eng_ eng_ 1 eng_ eng_ eng_ 1 eng_ engine _ engine _ ev, ev,,(), (),(),(), () ig 5 Strutural iagra for te exaut anifol () ig 4 Strutural iagra for te intae anifol ; (45) were: engine () = te tranfer funtion eterine by te atuator of te injetion u; engine ( ) = te tranfer funtion eterine by te loa engine; If Lalae -1 i alie to te ifferential equation (44) written above, te reult i te ifferential equation exreing te ynai engine oeration in relation to tie (equation 46), for te uerarge internal obution engine witout ajutent atuator for te turbine an oreor 11 EROENIA Sulient 1/13
6 , 4, 5 3 eng _ eng _ eng _ 1 at _inj _ u (46) at _inj _ u eng _ eng ainj a ev (47) at _ inj _ u a ev (48) ainj a eveng (49) ainjeng a ev ev ev (5) a ev ev ev eng ev at _inj_ u (51) igure 7 ow te trutural iagra of te ieel uerarge engine [8], oniere a te rotation of te autoati ajutent objet S,,, engine, engine,(),(),,() ig 6 Strutural iagra for te turboarger () () ig 7 Strutural iagra for te uerarge internal obution engine aing into aount te ifferent arge ee an ateatial oel of te engine ubyte, te reult yiel ifferent ateatial oel rereente by ifferential equation u to grae 5 Bae on tee oel, te ynai engine oeration of uerarge engine an be obtaine 3 ONLUSION On te bai of te ateatial oel of te ynai regie of te uerarge engine an te tranfer funtion etablie, te following onluion an be eifie: -- ranfer funtion woul allow te aieveent of an autoati yte ontrol loate on te engine, wi an ontrol all ynai an tationary regie an an enure te woring of te engine on otiu regie wit iniu oible fuel onution -- Uing an autoati yte ontrol for engine, te yte will enure quality inie for all te ynai regie of te wole engine an a ig yte erforane on tationary regie of oeration, wit iniu error for ee an aeleration e autoati yte ontrol will enure erforane for te wole engine an all it ubyte, uring tranitory regie of oeration REERENES [1] Buriu,, Internal obution iton Engine eroynai roee, urboarger, Oerating arateriti an Engine Intallation, Eurolu ubliing, Galati 6 [] Buriu,, alulation of te unteay eanial an gaoteroynai roee in te free rotation uerarger unit of te uerarge internal obution engine, Bulletin of te ranilvania Univerity of Braov, vol (51) erie I, 9 [3] Duitru, G, Buriu Buriu, S,, Dynaial arateriti of Suerarge Internal obution Engine Itelf, e ientifi eion in Univerity Dunarea e Jo, Galati 199 [4] Duitru, G, Dynaial arateriti of Aiion ie for Internal obution Engine, e ientifi eion in Univerity Dunarea e Jo, Galati 1993 [5] Duitru, G, Dynaial arateriti of Evauation ie for Internal obution Engine, e ientifi eion in Univerity Dunarea e Jo, Galati 1993 [6] Duitru G, Buriu, S,, Dynaial arateriti of urboarger for Internal obution Engine, e ientifi eion in Univerity Dunarea e Jo, Galati 1994 [7] Duitru G, Buriu, S,, Dynaial arateriti of Injetion Syte for Internal obution Engine, e ientifi eion in Univerity Dunarea e Jo, Galati 1995 [8] Buriu S, ei D, ontribution to te tuy of nontationary roee in te internal obution engine overloaing turbo-oreor, Univerity of Galati, aulty of eanial Engineering, Deartent of Internal obution Engine, EROENIA Sulient 1/13 113
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